@Nitish

you are thinking about particles made up of electrons

or protons. May be you have nuclear particles or atomic particles

in mind. This thread is however discussing elementary particles.

These particles have no spacial dimension in the ideal case if

you think of them classically. Quantum mechanically they have

de Broglie wave lengths characterized by their momentum.

The question is that, in this case, can you have charges if an

elementary particle is mass-less. I cannot think of any mass-less

particle which has electric charge. However I can think of mass-less

gluons which have QCD "color" charges.

Dear VF,

Please see discussion in the thread started by me.

Regards,

RP

According to the body and topic of the question, my answer will be limited to an abelian gauge theory—such as electrodynamics—with an arbitrary number of material (=non-gauge) fields, not restricted to those fields contained in the Standard Model.

The short answer is that charged, massless particles may in principle exist so long as their helicity is 1/2.

According to the totalitarian principle ("Everything not forbidden is compulsory", due to Gell-Mann in the context of physics) that governs quantum field theory, only symmetries can protect fields from acquiring mass through radiative corrections. In the case of massless scalars (helicity zero particle), this symmetry is a constant shift in field space. This means that only derivative terms of the scalar field may appear in the Lagrangian. The only way to achieve this together with the fact that the scalar is charged is that the scalar field is a Goldstone boson of the "spontaneously broken" abelian gauge symmetry (the name "spontaneously broken" is a bad one, in the case of gauge symmetries one should refer to it as an Englert–Brout–Higgs–Kibble mechanism). In this case, however, the massless scalar would actually be a longitudinal mode of the now massive gauge field (see abelian Higgs mechanism).

Helicity 1/2 fermions can be massless and charged. Chiral symmetry protects them form getting mass through quantum fluctuations. In the case of the Standard Model is more complicated because particles can acquire mass through the Higgs mechanism (I now mention only Higgs because it is the Standard Model Englert–Brout–Higgs–Kibble mechanism), so that one has to write all Yukawa interaction terms, involving scalars and fermions, so as to see what happens to the fermions after the scalar field gets its vacuum expectation value. I stop here.

The gauge field (the photon field in electrodynamics) itself has helicity 1 and is massless, but because it is an abelian gauge field, the particle doesn't have charge. Note, however, that this doesn't mean that photons cannot interact each other. They do interact through quantum processes (see photon-photon interaction) mediated by charged leptons. If the gauge symmetry were non-abelian, then the gauge particles would be charged. However, they would mediate short-range interactions because of confinement. They could also get mass from an Englert–Brout–Higgs–Kibble mechanism, as the Z and W's boson do in the Standard Model.

Finally, in relativistic quantum field theories, one can also have gravitons, which are massless and have spin 2 (with respect to a Minkowski background). If one considers energy-momentum as the "charge" of gravity, gravitons are then charged too.

According to me, charge develops due to presence of charge carrier (either electrons or protons or any other) and all of them have mass so it is difficult to find massless charged particles. (I thin so, but not sure)

Regards,

Nitish

@Nitish

you are thinking about particles made up of electrons

or protons. May be you have nuclear particles or atomic particles

in mind. This thread is however discussing elementary particles.

These particles have no spacial dimension in the ideal case if

you think of them classically. Quantum mechanically they have

de Broglie wave lengths characterized by their momentum.

The question is that, in this case, can you have charges if an

elementary particle is mass-less. I cannot think of any mass-less

particle which has electric charge. However I can think of mass-less

gluons which have QCD "color" charges.

Without entering into the theoretical considerations, it is hard to imagine a massless particle carrying charge as such a particle has to move with a speed of light. This would have some catastrophic consequences concerning the electromagnetic field, like ultraviolet divergence, alias infinite energy of virtual photons. I do not doubt that there is a more rigorous proof of this heurestic conjecture.

Hi all... just to talk about:

if it is true that then the answer, at least in principle, can be intended as "an answer at different levels of abstraction".

So the first thing Im wondering is if: each layer can deal with the matter in a particular way, and so excluding/avoiding arguments that are either not relevant to it nor related to different complexities.

For example: classically speaking the one could be the em wave interaction/emission by massive/masseless charged-particles (UV catastrophes?) This because in classical electrodynamics the only way to measure a charge is by using the em field. And to measure a mass we can only use motion-variations.

In the sense of QM (either not relativistic e.g. Schroedinger than relativistic and QFT) the spatial domain in which you can choose the working hypothesis is much broader. We can use the concepts of: Spin, Bosonic-Fermionic matter, group theories and symmetries, coupling constants (gauge for em) and so on.... I know that Majorana built up a theory relying on neutrinos .... as Dirac --> (cfr. http://arxiv.org/abs/0706.0052)

@ Adam Jacholkowski

For the case of gluons they are confined within the nucleus

of 10^{-13} cm. They are emitted by one quark and almost

instantly they are absorbed by another quark. In this way they

mediate strong force. In that sense even though they travel

at the speed of light, they cannot escape nuclear radius because

they are instantly absorbed. Energy of gluons is sum of kinetic

energy and interaction energy with quarks.

http://physics.stackexchange.com/questions/7905/massless-charged-particles

Massless charged particles can't exist in Nature because they would be easily produced by the colliders, and they haven't been. Such a production would simply arise from the Feynman diagram with an intermediate photon that "splits" into the new charged massless particle and its antiparticle. The cross section of this process would be calculable, and not small in any way.

Also, the fine-structure constant α=1/137.036, one expressing the strength of the electrostatic interactions in the natural units, is not a real constant. It's running. However, it's only running at energy scales such that there exist lighter charged particles. In Nature, it means that the constant is only running above the mass of the electron or positron - the lightest charged particles.

If there were massless charged particles, the electron and positron would become unstable - one problem - and the fine-structure constant would run to α=0 at very long distances - another problem, and it obviously doesn't. So massless charged particles are theoretically impossible in our world - assuming that we empirically know some things such as the fact that there is a limiting Coulomb force at long distances.

FWIW, electrons in graphene are behaving as if they are charged massless Dirac particles for a "speed of light" determined by the properties of grapheme (that is much lower than the usual speed of light).

Quite possible (it is out of my domain) but here we are talking about physical particles and not quasiparticles.

@Adam,

yes, I know, and I find your argument convincing. I would guess the loophole here is that the "speed of light" in graphene is not actually the speed at which excitations coupling to charge propagate in graphene.

The argument from @Kasim seems to suggest that the mass of any charged particles are experimentally bounded from below by the mass of the electron. Is there some theoretical first principles argument that says

m >= Universal constant * |q|

and even better, the inequality is an equality for electrons and positrons?

I would say that for any charged particle one has to include the contribution to its mass due to the energy of the e.m. field generated by its charge. There is therefore always at least this contribution to the mass of any charged particle, which thus can never be zero.

@Treleani. That is a good point. A long time ago I learned that the electron should have infinite mass because it is a "point particle" with a delta distribution of charge ,but quantum mechanics and the Heisenberg uncertainty relation saves the day by giving an intrinsic maximally peaked continuous distribution. However, the true contribution of the electric field to the mass of the electron would be determined by QCD, and I thought that renormalising the bare mass of the electron is one of the first things one does. So I am not sure. Can one actually compute this contribution?

Photons are, according to standard science, mass-less energy bundles, the same as electrons, protons, and neutrons are energy bundles, and which are the building blocks of the Universe.

Photons show electromagnetic properties, that is responses to charge and magnetic fields. They have a spin of 1.0, and they have twice the gravity than a standard particle of the same energy would have.

Ingo H. Leubner

@Ingo

Up to my knowledge (high energy) photons are not disturbed by magnetic and or electric fields of the LHC - Alice apparatus, for example, so one needs special absorbers (alias EM calorimeters) to detect them and measure their energy

http://lpsc.in2p3.fr/index.php/en/activites-scientifiques/alice-jlab/activites-techniques-alice-emcal/emcal-dans-lexperience-alice

The response of (low-energy) photons to magnetic and electric fields is text-book knowledge. I am intrigued that high-energy photons don't act the same way. Thank you for this information!

The double-gravity is due to the photon speed of light. Since gravity is anti-energy, the 'bending of space' and the associated models are interesting concepts, but not necessary. I will publish the modeling of the Big Bang, which changed the gravity understanding, at my Research-Gate site. Ingo

From quantum electrodynamics it can be found that photons cannot couple directly to each other, since they carry no charge, but they can interact through higher-order processes. A photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion–antifermion pair, to either of which the other photon can couple. This fermion pair can be leptons or quarks. Thus, two-photon physics experiments can be used as ways to study the photon structure, or what is "inside" the photon.

Set in this way it's impossible to answer. If by ``charged'' you mean ``electrically charged'', then the answer depends on the nature of the charged particle. If it's a scalar (spin 0) particle, then the answer was given by S. Coleman and E. Weinberg in 1973: quantum corrections lead to a mass for both scalar and photon.

If it's a spinor (spin 1/2) particle, charged under the abelian gauge field then things are more subtle. The reason is that the classical action of a massless spin 1/2 particle can be written as the sum of two actions of particles that don't interact with each other: the helicities of the spin 1/2. The interaction with the gauge field, also, splits into two terms. So, at a classical level, and by taking into account only perturbative effects, that are sensitive to the action, no mass term can be generated (that links the two chiralities).

The photon remains massless, protected by gauge invariance.

Now, if you look at the measure of the path integral, you'll find that it doesn't split into a product over the two helicity states: in the presence of the gauge field, you pick up a Jacobian. It is this Jacobian that will lead to a mass term for the spin 1/2, beyond perturbation theory. The reason is that the Jacobian is not invariant under chiral transformations and, therefore, will generate terms that are not invariant, either. One such term is the mass term for the spin 1/2. However the photon will remain massless, since gauge invariance is a symmetry of both action and measure.

Now in the ``real world'', the spin 1/2 leptons have the property that their two chiralities have different weak interactions: so the leptons would be massless. The only way they can acquire a mass is through their interaction with the Higgs boson, through the Brout-Englert-Higgs mechanism.

I suggest to consider electromagnetic (EM) mass, which was discussed in relation to the rest mass of the electron in early days of QED. This EM mass should come from the energy density of static electric field surrounding charged particle (also magnetic contribution from the dipole magnetic moment should be there for the electron). So particle having static electric charge should have mass in Vacuum regardless it interaction with Higgs field, I think.

@Nitish Ranjan...What about QUARKS they don't contain e or p, still have charge and mass...